论文标题
与多项式衰减相关性的区域保存表面差异性无处不在
Area preserving surface diffeomorphisms with polynomial decay of correlations are ubiquitous
论文作者
论文摘要
我们表明，任何表面都允许保存$ c^{1+β} $ diffemormormormist的区域，其非零lyapunov指数为bernoulli，并具有相关性多项式衰减。我们在相关性上同时建立上和下多项式界限。此外，我们表明这种差异性满足了中心极限定理，并且具有较大的偏差特性。最后，我们表明，我们构建的差异性具有独特的双曲线伯努利量度最大熵的度量，其具有指数性相关性的衰减。
We show that any surface admits an area preserving $C^{1+β}$ diffeomorphism with non-zero Lyapunov exponents which is Bernoulli and has polynomial decay of correlations. We establish both upper and lower polynomial bounds on correlations. In addition, we show that this diffeomorphism satisfies the Central Limit Theorem and has the Large Deviation Property. Finally, we show that the diffeomorphism we constructed possesses a unique hyperbolic Bernoulli measure of maximal entropy with respect to which it has exponential decay of correlations.
